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How much do you weigh? (Hint: it’s a trick question)

A friend of mine called yesterday morning to ask a favour: someone he knows read a thing about the upcoming eclipse on a NASA webpage, and about what difference this would make on our weight, and got the impression that there was a mistake in their calculations. The passage was the following:

Starting as an observer on the ground, you are under the gravitational influence of Earth, the moon and the sun. At the time of the August 21, 2017 eclipse, Earth will be 151.4 million kilometers from the sun, and the moon will be located 365,649 km from the surface of Earth. Using Newton’s Law of Gravity, we can calculate the force of the sun, moon and Earth on an 80 kg person. Earth accounts for 784.1 Newtons of force (176.42 pounds), the moon provides 0.0029 Newtons (0.01 ounces) and the sun provides 0.4633 Newtons (1.6 ounces). But because our Earth rotates, this also provides an ‘anti-gravity’ centrifugal force we can also calculate. So if we add the forces with their correct directions we get a total gravitational force of 784.1 — 0.0029 — 0.4633 = 783.634 Newtons or 176.317 pounds. So, you will be about 1.7 ounces lighter!

My friend asked me to check it out and report back to him so that he could pass on the information. So I did, and I thought it might be interesting to write it up, just in case you may be interested, and in case a similar question comes up again at some point in the future. If you are interested, you can read it here.